When using ourselves and another person as the subject of a sentence, we use their name first (like "John and I"); but when the same two people become the object of a sentence, which order should the ...

I know that "Would you mind… ?" (the Present Conditional) is more polite than "Do you mind…?" (the Simple Present), and also, that they have to be completed this way: "Do you mind if I do sth?/Would ...